Abstract:
For paraxial optical beams propagating in a medium whose parabolic transverse profile of dielectric permeability varies arbitrarily along the beam direction, universal invariants have been determined, i.e. certain integral values that remain valid along the beam axis independently of the particular dependence of the dielectric permeability on the coordinates. The effect of medium nonparabolicity on the invariants is discussed.

References:

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2. D. Marcuse. Optical Waveguides. Mir (1974).
   
3. V. V. Dodonov and V. I. Man'ko. Universal invariants of quantum systems and generalized uncertainty relations. In: Group Theoretical Methods in Physics, Vol. 2, pp. 11-33. Nauka, Moscow (1983).
   
4. V. V. Dodonov and V. I. Man'ko. Universal invariants of paraxial optical beams. In: Group Theoretical Methods in Physics, Vol. 2, pp. 434-435. Nauka, Moscow (1986).

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